Timeline for An $n!\times n!$ determinant
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Feb 14, 2012 at 17:22 | comment | added | Gjergji Zaimi | Where $c_T(k)$ is the content of the cell labelled $k$ in $T$. | |
| Feb 14, 2012 at 17:21 | comment | added | Gjergji Zaimi | You are correct. So another way of saying this is that our polynomial is (up to sign of x) the product of JM's characteristic polynomials, and the spectrum of $J_k$ in $V^{\lambda}$ is $\lbrace c_T(k): T\in SYT(\lambda)\rbrace$, by Okounkov-Vershik. | |
| Feb 14, 2012 at 17:09 | comment | added | Igor Makhlin | ... $\omega=(x+J_1)(x+J_2)\cdots(x+J_n)$ ... Am I talking nonsense, or this means that our polynomial is (up to the sign of $x$) the product of the JM's characteristic polynomials (as of operators on $\mathbb{C}[S_n]$) which are known to be polynomials of the needed type (mathoverflow.net/questions/83150/…)? | |
| Feb 14, 2012 at 16:01 | comment | added | Gjergji Zaimi | I gave a link to the original paper with the theorems. | |
| Feb 14, 2012 at 16:01 | history | edited | Gjergji Zaimi | CC BY-SA 3.0 |
added 197 characters in body
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| Feb 14, 2012 at 14:33 | comment | added | darij grinberg | I'd love to see all these Jucys theorems proven somewhere... but I guess I'm just too lazy to go in the library. | |
| Feb 14, 2012 at 9:31 | history | answered | Gjergji Zaimi | CC BY-SA 3.0 |